如何检查向量是否在两个向量内 [英] How to check if a vector is within two vectors

问题描述

这是一张图片:

我有两个向量:os，oe

I have two vectors : os, oe

它们之间的范围始终是从os(开始)到oe(结束).

the range between them is always from os (start) to oe (end).

因此，在此图像中，范围为270°.

So in this image the range between is a angle of 270°.

然后我要检查两个向量:oa，ob

Then I have two vector to check: oa, ob

您可以看到向量oa应该在osoe形成的范围内，向量ob应该在osoe之外.

As you can see the vector oa should be within the range formed by osoe and the vector ob should be outside.

我想知道是否有一种方法可以仅使用矢量数学(例如叉积点积)进行检查.

I am wondering if there is a way to do the check using only vector math (such as cross product dot product).

我试图将叉积与顺时针/逆时针检查一起使用，但是当两者之间的夹角大于180°时，情况就变得复杂了.

I tried to use cross product with clockwise/counter clockwise check but it seems like when the angle in between is larger then 180°, things get complex.

任何建议将不胜感激，谢谢:)

Any advice will be appreciated, thanks :)

推荐答案

我将指向 p 的向量表示为 op.

I denote vector to point p as op.

计算叉积

 c_se = cross(os, oe)

如果 c_se> = 0 (角度位于 0..180范围)，那么您必须检查是否

If c_se>=0 (angle in 0..180 range), then you have to check whether

cross(os, op) >= 0 AND cross(op, oe) >= 0

如果 c_se<0 (角度在 180..360范围中)，那么您必须检查是否

If c_se < 0 (angle in 180..360 range), then you have to check whether

NOT (cross(oe, op) >= 0 AND cross(op, os) >= 0)

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